不確実性下における分布ロバストリアプノフ関数探索
Distributionally Robust Lyapunov Function Search Under Uncertainty
未知の分布に従う外乱を受ける動的システムに対し、有限の外乱サンプルから分布ロバストなリアプノフ関数を探索する手法を提案し、SOS制約やニューラルネットワークによる定式化を示した。
著者: Kehan Long, Yinzhuang Yi, Jorge Cortes, Nikolay Atanasov
分類: math.OC, cs.RO
原文アブストラクト
This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.
